Abstract : In a previous paper, the dynamic, steady-state propagation of an semi-infinite anti-plane shear crack was considered for an infinite, general linearly viscoelastic body. Under the assumptions that the shear modulus is a positive, non-increasing continuous and convex function of time, convenient, closed-from expressions were derived for the stress intensity factor and for the entire stress distribution ahead of and in the plane of the advancing crack. The solution was shown to have a simple universal dependence upon the shear modulus and crack speed from which qualitative information can readily be gleaned. Here, the corresponding problem for a general, linearly viscoelastic layer is solved. An infinite series representation for the stress intensity factor is derived, each term of which can be calculated recursively in closed-form. As before, a simple universal dependence upon crack speed and material properties is exhibited. (Author)